Primordial black hole formation in the matter-dominated phase of the Universe

TL;DR

This paper studies how primordial black holes form during the matter-dominated phase of the universe, highlighting the importance of nonspherical effects and providing formulas for their production probability.

Contribution

It introduces a new analysis of PBH formation in matter domination using the Zel'dovich approximation and derives a semi-analytic formula for production probability applicable even for large density fluctuations.

Findings

Production probability is much higher in matter domination for small fluctuations.

Derived a semi-analytic formula for probability when fluctuations are small.

Compared matter and radiation era probabilities, finding they are similar for larger fluctuations.

Abstract

We investigate primordial black hole formation in the matter-dominated phase of the Universe, where nonspherical effects in gravitational collapse play a crucial role. This is in contrast to the black hole formation in a radiation-dominated era. We apply the Zel'dovich approximation, Thorne's hoop conjecture, and Doroshkevich's probability distribution and subsequently derive the production probability $\beta_{0}$ of primordial black holes. The numerical result obtained is applicable even if the density fluctuation $\sigma$ at horizon entry is of the order of unity. For $\sigma\ll 1$, we find a semi-analytic formula $\beta_{0}\simeq 0.05556 \sigma^{5}$, which is comparable with the Khlopov-Polnarev formula. We find that the production probability in the matter-dominated era is much larger than that in the radiation-dominated era for $\sigma\lesssim 0.05$, while they are comparable with each other for $\sigma\gtrsim 0.05$. We also discuss how $\sigma$ can be written in terms of primordial curvature perturbations.